Chapter 5.1, Problem 73AYU

(a)

To determine

To find: The function that relates dollars to Euros.

Answer to Problem 73AYU

  $f\left(x\right)=0.7045x$

Explanation of Solution

Given: Trades often buy foreign currency in hope of making money when the currency’s value changes. On march 22, 2011, one U.S. dollar could purchase 0.7045 Euros, and one Euros could purchase 114.9278 yen.

Let $f\left(x\right)$ represent the number of Euros with $x$ dollars.

Let $g\left(x\right)$ represent the number of yen with $x$ Euros.

According to question, one U.S. dollar could purchase 0.7045 Euros

Therefore, $x$ dollars could be $0.7045x$ Euros.

Thus, $f\left(x\right)=0.7045x$

(b)

To determine

To find: The function that relates Euros to Yen.

Answer to Problem 73AYU

  $g\left(x\right)=114.9278x$

Explanation of Solution

Given: Trades often buy foreign currency in hope of making money when the currency’s value changes. On march 22, 2011, one U.S. dollar could purchase 0.7045 Euros, and one Euro could purchase 114.9278 yen.

Let $f\left(x\right)$ represent the number of Euros with $x$ dollars.

Let $g\left(x\right)$ represent the number of yen with $x$ Euros.

According to question, one Euro could purchase 114.9278 yen.

Therefore, $x$ Euros could be $114.9278x$ Euros.

Thus, $g\left(x\right)=114.9278x$

(c)

To determine

To find: The function that relates Dollars to Yen.

Answer to Problem 73AYU

  $h\left(x\right)=80.9667x$

Explanation of Solution

Given: Trades often buy foreign currency in hope of making money when the currency’s value changes. On march 22, 2011, one U.S. dollar could purchase 0.7045 Euros, and one Euro could purchase 114.9278 yen.

Let $h\left(x\right)$ represent number of Yen with $x$ dollars.

  $\begin{array}{l}\text{Dollar to Euros}\\ f\left(x\right)=0.7045x\end{array}$

  $\begin{array}{l}\text{Euros to Yen}\\ g\left(x\right)=114.9278x\end{array}$

Now, find Dollar to Yen. That is, $\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)$

  $\therefore h\left(x\right)=g\left(f\left(x\right)\right)$

  $\begin{array}{l}h\left(x\right)=114.9278\left(0.7045x\right)\\ h\left(x\right)=80.9667x\end{array}$

(d)

To determine

To find: The value of function $g\left(f\left(1000\right)\right)$ .

Answer to Problem 73AYU

In 1000 dollars purchased 80966.7 Yen.

Explanation of Solution

Given: Trades often buy foreign currency in hope of making money when the currency’s value changes. On march 22, 2011, one U.S. dollar could purchase 0.7045 Euros, and one Euro could purchase 114.9278 yen.

Put $x=1000$ in $h\left(x\right)$

Where, $x$ represents number of dollars and $g\left(f\left(1000\right)\right)$ represent number of Yen.

  $\begin{array}{c}h\left(1000\right)=g\left(f\left(1000\right)\right)\\ g\left(f\left(1000\right)\right)=80.9667\times 1000\\ =80966.7\end{array}$

In 1000 dollars purchased 80966.7 Yen.